MAT 2348 Midterm: MAT2348 exam.mat2348.2016-q
Document Summary
[4: let n be a positive integer. How many arrange- ments can we make using all the elements of this multiset: consider the unit paths of length 9 from the origin to somewhere. How many di erent points (a, b, c) are possible endpoints of such paths in r3: consider multisets of size 9 made up of any (non-negative) number of a"s and b"s and c"s. How many di erent such multisets are there: let pa,b,c be the number of unit paths from the origin to (a, b, c) in r3. [5: give a combinatorial proof that (cid:18)n + 1 k + 1(cid:19) = n + 1 n k(cid:18) n not use any factorials, nor indeed make any reference to any formula for (cid:18)a k + 1(cid:19). In particular, your answer should b(cid:19) other than the fact that it is the number of b-subsets contained in an a-set.
